Rectangle/Symmetry Problem

The diagram is just a rough representation. ABCD is a rectangle with BC = 4 and AB = 6. Points P, Q, and R are different points on a line that is parallel to line AD. Points P and Q are symmetric about line AB and points Q and R are symmetric about line CD. What is the length of line PR?

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I know I must be missing something simple... I've tried several things such as triangles using the diagonal of the rectangle. I also tried this:

Let x equal the distance between point Q and line AB.
Let 4-x equal the distance between point Q and line CD.